Example. In a problem I was working on, I had an expression of the form $(1-e^{-\alpha n})^{e^{\beta n }}$. I wanted to find an upper bound $f(\alpha, \beta, n)$ on this that makes it easier to see conditions on $\alpha$ and $\beta$ that make this expression go to $0$ in the limit $n\to \infty$ (I have found a good bound by now).
My question isn’t what such a bound is in this case (I've already found one), but rather, how does one go about finding useful bounds in situations like this, without having to re-invent the wheel?
Are there standard references with tables or lists of various useful inequalities? i.e. references that professional mathematicians look to if they don't know a useful bound off the cuff (similar to tables of known integrals, or tables of moments of specific probability distributions).
